Iterative State Estimation in Non-linear Dynamical Systems Using Approximate Expectation Propagation
Authors: Sanket Kamthe, So Takao, Shakir Mohamed, Marc Peter Deisenroth
TMLR 2022 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We use a classic non-linear system benchmark, the uniform nonlinear growth model (UNGM) (Doucet et al., 2000) with a fixed seed as a running example to illustrate properties of the iterative smoothing scheme. The article is organised as follows. In Section 2, we establish the notation and review classic Kalman filtering and smoothing, which we then apply to the UNGM benchmark. ... We compare the results of EP with the unscented Kalman filter and smoother (van der Merwe & Wan (2004)). Results are shown in Figure 1, where we plotted the root mean square error (RMSE) and the negative log-likelihood (NLL) of its predictions, all measured in latent space x (see Appendix A.3 for the precise expressions of these metrics). |
| Researcher Affiliation | Collaboration | Sanket Kamthe EMAIL Department of Computing, Imperial College London Chief Technology Office, JP Morgan Chase. So Takao EMAIL UCL Centre for Artificial Intelligence, University College London. Shakir Mohamed Department of Computer Science, University College London. Marc Peter Deisenroth UCL Centre for Artificial Intelligence, University College London. Equal contribution. Also with Deep Mind. |
| Pseudocode | Yes | Algorithm 1 Gaussian EP for Dynamical Systems |
| Open Source Code | Yes | Code available at https://github.com/sanket-kamthe/EPy State Estimator |
| Open Datasets | Yes | We use a classic non-linear system benchmark, the uniform nonlinear growth model (UNGM) (Doucet et al., 2000)... We now test our proposed method for a classic bearings-only tracking problem that is commonly encountered in passive sensor environments... similar to the example considered in Särkkä & Hartikainen (2010)... In our final example, we test our method on the Lorenz 96 model (Lorenz, 1996), another commonly used benchmark for nonlinear filters/smoothers (Brajard et al., 2020; Fablet et al., 2021; Ott et al., 2004). |
| Dataset Splits | No | The paper describes using established benchmark models (UNGM, bearings-only tracking, Lorenz 96) and specifies trajectory lengths and initial state distributions, but does not provide explicit training/test/validation splits in the traditional sense for data partitioning (e.g., percentage splits or sample counts). |
| Hardware Specification | No | The paper does not provide specific details about the hardware (e.g., CPU, GPU models, or memory) used to run the experiments. |
| Software Dependencies | No | The paper mentions general techniques and algorithms but does not specify any particular software libraries, programming languages, or their version numbers used for implementation. |
| Experiment Setup | Yes | The unscented transform for a single seed. ... For the scaled UT we use parameters (αUT, βUT, κUT) = (1, 2, 3) for the transition function and (αUT, βUT, κUT) = (1, 2, 2) for the measurement function throughout the paper. ... We used 104 samples throughout this paper. ... Changing the damping rate to γ = 0.9... In Figure 4c, we use α = 0.9 and damping γ = 0.9... The parameters of the scaled UT were set to (αUT, βUT, κUT) = (1, 0, 1)... The model error covariance is Q = 0.1I. For the measurement model, we consider the quadratic operator h(x) = (x2 1, . . . , x2 d) Rd, with error covariance R = I. ... We used the values α {0.1, 0.8, 1.0} for the power factor and took 10 EP iterations with no damping for all the experiments. |